|
| |
|
|
A034385
|
|
Expansion of (1-16*x)^(-1/4), related to quartic factorial numbers.
|
|
6
|
|
|
|
1, 4, 40, 480, 6240, 84864, 1188096, 16972800, 246105600, 3609548800, 53421322240, 796463349760, 11946950246400, 180123249868800, 2727580640870400, 41459225741230080, 632253192553758720
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
Seiichi Manyama, Table of n, a(n) for n = 0..500
A. Straub, V. H. Moll, T. Amdeberhan, The p-adic valuation of k-central binomial coefficients, Acta Arith. 140 (1) (2009) 31-41, eq (1.10)
|
|
|
FORMULA
|
a(n) = (4^n/n!)*A007696(n), n >= 1, a(0) := 1, A007696(n)=(4*n-3)(!^4) := product(4*j-3, j=1..n); G.f.: (1-16*x)^(-1/4).
D-finite with recurrence: n*a(n) +4*(-4*n+3)*a(n-1)=0. - R. J. Mathar, Jan 28 2020
|
|
|
MATHEMATICA
|
CoefficientList[Series[1/Surd[1-16x, 4], {x, 0, 20}], x] (* Harvey P. Dale, Aug 06 2018 *)
|
|
|
CROSSREFS
|
Cf. A007696.
Expansion of (1-b^2*x)^(-1/b): A000984 (b=2), A004987 (b=3), this sequence (b=4), A034688 (b=5), A004993 (b=6), A034835 (b=7), A034977 (b=8), A035024 (b=9), A035308 (b=10).
Sequence in context: A304447 A002705 A235372 * A249927 A218302 A296100
Adjacent sequences: A034382 A034383 A034384 * A034386 A034387 A034388
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
Wolfdieter Lang
|
|
|
STATUS
|
approved
|
| |
|
|
